KIKARAKU - Geometry Puzzles

Geometry that overturns your intuition.

KIKARAKU is an educational app that lets you experience counterintuitive geometry with your own hands. Answer with your gut first, move the shapes to check, then work out why it happens using the geometry you learned at school.

Developer: Fuji Bit Inc.

KIKARAKU is the 11th app in the "-raku" series of educational apps, and its theme is geometry. It covers 14 puzzles that most people get wrong on instinct, and every one of them unfolds in four phases.

Four phases:
1. Gut check: Answer with your gut first. Most people get these wrong.
2. Hands-on: Move the shapes with sliders and buttons, and watch your intuition get overturned.
3. Explanation: Familiar tools such as the circumference formula and the Pythagorean theorem turn the surprise into understanding, with diagrams and formulas.
4. Final check: Answer a challenge question to clear the stage.

14 geometry puzzles (3 categories):

Shapes in motion
- Angle Puzzles (The Sum of Exterior Angles): do the exterior angles of any polygon add up to 360°?
- Secrets of Triangles (Napoleon's Theorem): a hidden equilateral triangle in every triangle?
- Symmetry & Motion (The Coin Rotation Paradox): roll a coin around an identical one; how many turns?
- Circle Theorems (The Rope Around the Earth): add 1 m to a rope around the Earth; how big is the gap?
- Constant Width (The Reuleaux Triangle) (new): is the circle the only shape of constant width?

Tricks of length and area
- Pythagoras (The Missing Square): how can the same pieces seem to gain a square?
- Tangram (Same Area, Different Perimeter): same area, very different perimeters?
- Area Master (Same Perimeter, Different Area): which shape holds the most area for a fixed string?
- Nets (The Spider and the Fly): find the shortest path across a box by unfolding it.
- Coordinate Geometry (Taxicab Geometry): measure along city streets, and a circle becomes a square?

Numbers hidden in shapes
- Similarity & Ratio (The Square-Cube Law): a giant twice as tall weighs eight times as much?
- The Golden Ratio (The Golden Angle and Sunflowers): why do sunflowers turn by about 137.5°?
- Volume & Surface Area (Gabriel's Horn): a horn you can fill with paint but never paint.
- Geometry & Chance (Buffon's Needle) (new): drop needles on a floor and pi appears.

Features:
- A clean, modern design (switch between dark and light themes)
- A home screen by category that records the stages you have cleared
- Every stage advances in four phases, and you can always see where you are
- If you go back during the final check, the app asks whether to leave the stage
- Available in 74 languages, including English and Japanese (follows your device language)
- No sign-in; start right away
- The puzzles work offline (the network is used only for ads)

Great for students learning geometry, teachers looking for classroom material, and anyone who enjoys a mathematical "wait, really?"

Price and purchases:
- Price: Free
- In-app products and subscriptions: None
- Ads: Banner ads by Pangle at the bottom of the screen, and a full-screen (interstitial) ad may be shown when you clear a stage
- On first launch, the app asks whether ads may be personalized. You can change this at any time in "About this app" > "Ad settings"

The "-raku" series of educational apps (selection): SUUGAKU (mathematics), BUTURAKU (mechanics), DENRAKU (electromagnetism), HARAKU (waves), NETURAKU (thermodynamics), KORAKU (optics), RYURAKU (fluid dynamics), KAKURAKU (probability), KIKARAKU (geometry)